Bishop Bernard Fellay, superior of the Society of St. Pius X, is pictured near an image of St. Pius X at the society's headquarters in Menzingen, Switzerland, May 11, 2012. (CNS/Paul Haring)

Vatican City — Pope Francis has met with the leader of a traditionalist group of Catholic bishops and priests who have been separated from the wider church for decades in opposition to the reforms of the Second Vatican Council, the Vatican has confirmed.

The pontiff met with Bishop Bernard Fellay, the Superior General of the Society of St. Pius X, Vatican press office deputy director Gregory Burke told journalists Monday. The Society said Francis and Fellay had met the afternoon of Friday, April 1.

Founded by the late French Archbishop Marcel Lefebvre in 1970, the Society widely rejects the teachings of the Council, a 1962-65 gathering of the world’s Catholic bishops that led to large reforms in the church’s liturgy and its stance towards the world.

Pope Benedict XVI had sought to repair relations with the group, lifting the excommunications of four of their bishops in 2009. Those efforts ultimately failed when Fellay rejected a doctrinal statement drafted by the Vatican for the group to sign.

In a recent interview posted on the Society’s website, Fellay said he thinks Francis may consider his group as existing on the "periphery" and thus needing to be accompanied back to the church.

"[The pope] uses the expression ‘walk forward’ with people on the periphery, hoping to manage to improve things," said Fellay. "Therefore it is not a fixed decision to succeed immediately: a development, a walk, goes wherever it goes."

"It is clear that Pope Francis wants to let us live and survive," the bishop continued. "He even said to anyone who cares to listen that he would never do the Society any harm."

Francis had indicated a move toward unity between the wider church and the traditionalist society with the opening of the ongoing Jubilee year of mercy last fall.

In a September letter to the Pontifical Council for the Promotion of the New Evangelization, which is organizing the holy year on his behalf, he explained that members of the society would be granted faculties during the year to offer absolution of sins "validly and licitly" to those who approach them for confession.

"This Jubilee Year of Mercy excludes no one," the pontiff said then. "I trust that in the near future solutions may be found to recover full communion with the priests and superiors of the Fraternity."

In his recent interview, Fellay said he and the society were seeking to have “a clear definition sometime of this term ‘full communion.’”

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Italian newspaper Il Foglio cited sources who said the meeting between Francis and Fellay Saturday "was positive" and that the "understanding is good" between the two leaders.

Outside of the faculties granted during the Jubilee year, members of the traditionalist Society are considered not to be in full communion with Rome and, in normal circumstances, its priests and bishops cannot exercise Roman Catholic ministry.